Twin-engined rotorcrafts are generally provided with two free-turbine turboshaft engines. Power is then taken from a low pressure stage of each free turbine that rotates at about 20,000 revolutions per minute (rpm) to about 50,000 rpm. Thereafter, a gearbox is necessary to connect the free turbines to the main rotor that provides lift and propulsion since the speed of rotation of the rotor lies substantially in the range 200 rpm to 400 rpm: this is the main gearbox (MGB). It is also desirable to balance power from the engines so that each engine delivers identical power to the MGB.
Thermal limitations on engines and torque limitations on the MGB enable three normal operating ratings to be defined for use with turboshaft engines:                a takeoff rating that can be used for five to ten minutes, corresponding to a level of torque for the gearbox and to a level of heating for each engine that can be accepted for a limited length of time without significant damage: this is the maximum takeoff power (PMD);        a maximum continuous rating such that the capacities of the main gearbox and those that result from the maximum heating that is acceptable on a continuous basis upstream of the high pressure blades of the first stage of each free turbine are not exceeded at any time: this is the maximum continuous power (PMC); and        a maximum transient rating, set by regulation: this is known as the maximum transient power (PMT).        
There also exist super contingency ratings when one of the two engines fails:                a super contingency rating during which the capabilities of the main gearbox on the inlet stages and the thermal capabilities of the turboshaft engine are used to the maximum: this is referred to as super-emergency power (PSU), it can be used during 30 seconds consecutively at the most, and three times during a flight. Using the PSU requires the engine to be removed and overhauled;        a super contingency rating during which the capabilities of the main gearbox on its inlet stages and the capabilities of the turboshaft engine are used very fully: this is referred to as maximum emergency power (PMU) that can be used for 2 minutes following PSU, or for a maximum of 2 minutes and 30 seconds consecutively; and        a super contingency rating during which the capabilities of the main gearbox on the inlet stages and the thermal capabilities of the turboshaft engine are used without damage: this IS referred to as intermediate emergency power (PIU) and can be used for 30 minutes or continuously for the remainder of the flight after the engine has failed.        
The engine manufacturer uses calculation and testing to draw up available power curves for a turboshaft engine as a function of altitude and outside temperature, and does so for each of the above-defined ratings.
In addition, the manufacturer determines the limitations of the turboshaft engine that make it possible to obtain a minimum power for each of the above-specified ratings and an acceptable lifetime, the minimum power corresponding in particular to the power developed by a turboshaft engine that is old, i.e. an engine that has reached its maximum lifetime. These limits are generally monitored by means of three surveillance parameters of the engine: the speed of rotation of the engine's gas generator; the engine torque; and the ejection temperature of the gas at the inlet to the free turbine of the engine, which parameters are respectively known as Ng, Cm, and T45 to the person skilled in the art.
To monitor these limits, document FR 2 749 545 discloses a piloting indicator that identifies amongst the surveillance parameters of the turboshaft engine, which parameter is the parameter closest to its limit. The information relating to which limitations are to be complied with is thus grouped together on a single display, thereby making it possible firstly to obtain a summary and present only the result of the summary so as to simplify the task of the pilot, and secondly to save space on the instrument panel. This produces a “limiting parameter” amongst said surveillance parameters of the engine, i.e. the parameter whose current value is the closest to the corresponding limit value. That is why such an indicator is also referred to below as a first limitation indicator or “IPL”.
Furthermore, variants of such an IPL serve to display the value of the limiting parameter as an equivalent power, i.e. in terms of a power margin such as +10% of PMD, for example, or else as a pitch margin, where pitch indicates the position of the rotor blades of the rotorcraft relative to the incident air flow.
Furthermore, whatever the rating, turboshaft engines are piloted by using a piloting parameter selected by the manufacturer from the above-mentioned surveillance parameters, representative of the operation of the engine both during a stage of stabilized use and during a transient phase.
A relationship for limiting the piloting parameter as a function of altitude and of outside pressure can then be defined so as to ensure that none of the surveillance parameters exceeds its limit in most configurations, e.g. when flying in hot weather.
In this context, balancing the engines of a twin-engined rotorcraft is generally performed by aligning the values of the piloting parameter for both engines. Consequently, if the piloting parameter is the speed of rotation Ng, for example, then balancing is achieved when both engines have the same speed of rotation Ng. That does not constitute a genuine balance, but rather a mere alignment. Aligning the piloting parameters of the engines does not guarantee that their powers will be in balance, since the engines might be operating in significantly different manners.
It should be observed that the engines of the latest generation are controlled by controlling electronic computers known as full-authority digital engine control (FADEC) by the person skilled in the art, serving to determine the position of a fuel metering unit as a function firstly of a regulation loop including a primary loop based on maintaining the speed of rotation of the rotorcraft rotor, and secondly on a secondary loop based on a setpoint value for the piloting parameter. Such FADECs then implement the principle of balancing, or rather aligning, as mentioned above, by determining setpoint values for the piloting parameter of each engine that are very close to each other.
Balancing on those lines is effective but reveals limitations.
Firstly, the engines are continuously balanced on the basis of the value of the same surveillance parameter, namely the piloting parameter. Unfortunately, experience shows that depending on flying conditions, the surveillance parameter that is the most pertinent for achieving balance differs.
Secondly, that principle does not enable engine performance to be optimized. For example, it can happen that maximum power is not reached on the two engines when piloting as a function of torque limitation.
Finally, that principle for balancing appears to be inappropriate if the piloting parameter is the temperature T45 at which gas is ejected or is torque Cm. The relationship associating torque and temperature varies as an engine ages, so it becomes difficult to balance two engines if they do not present the same degree of aging.